Adjacent Angles: Identifying Intersecting Lines in Geometric Diagram

To determine if the diagram shows adjacent angles, we need to analyze the geometric arrangement shown:

• Step 1: Identify the common vertex.

  In the diagram, both the vertical line and the diagonal line intersect at a point. This intersection point serves as the common vertex for the angles in question, as they radiate outward from this shared point.

• Step 2: Identify the common side.

  Adjacent angles must share a common side or arm. In the diagram, the vertical line acts as one common side for both angles, with one angle extending upwards and the other horizontally from the vertex.

• Step 3: Ensure no overlap of interiors.

  It is equally essential to ensure that these two angles do not overlap. Each angle branches from the vertex in a different direction, maintaining distinct interiors.

By confirming the presence of a common vertex and a common side without overlap of the angle interiors, the angles satisfy the definition of being adjacent.

Therefore, the diagram does indeed show adjacent angles.

Consequently, the correct answer is Yes.